Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn n-Tardy Sets
116
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Harrington and Soare introduced the notion of an n-tardy set. They showed that there is a nonempty $mathcal{E}$ property Q(A) such that if Q(A) then A is 2-tardy. Since they also showed no 2-tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete. Our study of n-tardy sets takes off from where Harrington and Soare left off. We answer all the open questions asked by Harrington and Soare about n-tardy sets. We show there is a 3-tardy set A that is not computed by any 2-tardy set B. We also show that there are nonempty $mathcal{E}$ properties $Q_n(A)$ such that if $Q_n(A)$ then A is properly n-tardy.
rate research
Read More
It is shown, from hypotheses in the region of $omega^2$ Woodin cardinals, that there is a transitive model of KP + AD$_mathbb{R}$ containing all reals.
We prove that a wide Morley sequence in a wide generically stable type is isometric to the standard basis of an $ell_p$ space for some $p$.
Soare proved that the maximal sets form an orbit in $mathcal{E}$. We consider here $mathcal{D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer. Some orbits of $mathcal{D}$-maximal sets are well understood, e.g., hemimaximal sets, but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the $mathcal{D}$-maximal sets. Although these invariants help us to better understand the $mathcal{D}$-maximal sets, we use them to show that several classes of $mathcal{D}$-maximal sets break into infinitely many orbits.
In this paper the Erdos-Rado theorem is generalized to the class of well founded trees.
We prove that for every Scott set $S$ there are $S$-saturated real closed fields and models of Presburger arithmetic.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
